A symmetry‐mode description of rigid‐body rotations in crystalline solids: a case study of Mg(H2O)6RbBr3. (1st April 2014)

• Record Type: Journal Article
• Authors: Müller, Melanie; Dinnebier, Robert E.; Dippel, Ann‐Christin; Stokes, Harold T.; Campbell, Branton J.
• Is Part Of: Journal of applied crystallography. Volume 47:Part 2(2014:Apr.)
• Page Start: 532
• Page End: 538
• Publication Date: 2014-04-01
• Subjects: Crystallography -- Periodicals; 548.05
• DOI: 10.1107/S1600576713034560
• Languages: English
• ISSNs: 0021-8898

Abstract

<abstract abstract-type="main" xml:lang="en"> <title> <x xml:space="preserve">Abstract</x> </title> <p>The application of rotational symmetry modes to quantitative rigid‐body analysis is demonstrated for octahedral rotations in Mg(H<sub>2</sub>O)<sub>6</sub>RbBr<sub>3</sub>. Rigid‐body rotations are treated as axial‐vector order parameters and projected using group‐theoretical methods. The high‐temperature crystal structure of the Mg(H<sub>2</sub>O)<sub>6</sub>RbBr<sub>3</sub> double salt consists of a cubic perovskite‐like corner‐sharing network of RbBr<sub>6</sub> octahedra with isolated MgO<sub>6</sub> octahedra at the perovskite <italic>A</italic> sites. A phase transition occurs at 411 K upon cooling, whereupon the MgO<sub>6</sub> octahedra experience a substantial rigid‐body rotation, the RbBr<sub>6</sub> octahedra are translated but not rotated, and both types of octahedra become slightly distorted. The MgO<sub>6</sub> rotation has three orthogonal components associated with the <italic>X</italic><sub>5</sub><sup>−</sup>, Γ<sub>4</sub><sup>+</sup> and <italic>X</italic><sub>1</sub><sup>−</sup> irreducible representations of the parent <inline-graphic xlink:href="ark:/27927/pgg55053hnj" mimetype="image" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /> space‐group symmetry which, given the weakly first‐order character of the transition, appear to be strongly coupled. Parametric and sequential refinements of the temperature‐dependent structure were conducted using four model types: (1) traditional atomic <italic>xyz</italic> coordinates for each atom, (2) traditional rigid‐body parameters, (3) purely displacive symmetry modes and (4) rigid‐body rotational symmetry modes. We demonstrate that rigid‐body rotational symmetry modes are an especially effective parameter set for the Rietveld characterization of phase transitions involving polyhedral rotations.</p> </abstract>